Congrats on your new acquisition. It appears you have some bulging in the right side (3 o'clock) of the chamber from dry-firing too much over the last 1.5+ centuries. That will need to be cleaned up to allow your case to chamber. You could do it with a chamber reamer ($$$) or VERY CAREFUL file work with a rounded file. There also seem to various dings in the chamber at 6 and 8 o'clock which also may need to be smoothed out.
The chip out of the chamber on the left side is fairly common and, in part because of the low pressure of the cartridge, should not pose a problem, although I would recommend that you always have the extractor installed when firing, as that provides some support to the remaining thin metal. However, your chamber ahead of the chip looks a little rough--perhaps some metal folded over--and may also need some cleaning up.
The scratches in the chamber (at least they look like scratches) could perhaps use a little sanding/smoothing.
With all the little chamber issues, it might be worthwhile to take it to a gunsmith, because all of these clean-ups will require careful work. I know you were hoping to avoid this, but if you found a smith with Spencer experience or, better yet, a chamber reamer, it should be a fairly simple job. But again, it calls for care and patience if you do it with files and abrasives. If you don't have experience with gunsmithing or fine metalwork, I would encourage you to team up with someone who does. Remember, any metal you file away was originally put there for a purpose, and once you cut it away, it cannot easily be added back.
The Starline cases can be hit-or-miss with original Spencers. The rim is a little undersize for the blade extractors--some seem to work and some don't, which is probably a function of manufacturing tolerances. They're not dangerous to shoot, but you might have something of a single-shot if the extractor can't get a bite on the rim.
Show us some more photos, and good luck with your new piece of history.
--DJ
(modified 29 JUN to correct typo)